Generalised Variance Function Estimation for Binary Variables in Large‐Scale Sample Surveys

Generalised variance function (GVF) models are data analysis techniques often used in large‐scale sample surveys to approximate the design variance of point estimators for population means and proportions. Some potential advantages of the GVF approach include operational simplicity, more stable sampling errors estimates and providing a convenient method of summarising results when a high number of survey variables is considered. In this paper, several parametric and nonparametric methods for GVF estimation with binary variables are proposed and compared. The behavior of these estimators is analysed under heteroscedasticity and in the presence of outliers and influential observations. An empirical study based on the annual survey of living conditions in Galicia (a region in the northwest of Spain) illustrates the behaviour of the proposed estimators.     

Tests for Symmetric Error Distribution in Linear and Nonparametric Regression Models

In linear and nonparametric regression models, the problem of testing for symmetry of the distribution of errors is considered. We propose a test statistic which utilizes the empirical characteristic function of the corresponding residuals. The asymptotic null distribution of the test statistic as well as its behavior under alternatives is investigated. A simulation study compares bootstrap versions of the proposed test to other more standard procedures.     

Variable selection in quantile regression when the models have autoregressive errors

This paper considers a problem of variable selection in quantile regression with autoregressive errors. Recently, Wu and Liu (2009) investigated the oracle properties of the SCAD and adaptive-LASSO penalized quantile regressions under non identical but independent error assumption. We further relax the error assumptions so that the regression model can hold autoregressive errors, and then investigate theoretical properties for our proposed penalized quantile estimators under the relaxed assumption. Optimizing the objective function is often challenging because both quantile loss and penalty functions may be non-differentiable and/or non-concave. We adopt the concept of pseudo data by Oh et al. (2007) to implement a practical algorithm for the quantile estimate. In addition, we discuss the convergence property of the proposed algorithm. The performance of the proposed method is compared with those of the majorization-minimization algorithm (Hunter and Li, 2005) and the difference convex algorithm (Wu and Liu, 2009) through numerical and real examples.     

Genetic Algorithm in the Wavelet Domain for Large p Small n Regression

Many areas of statistical modeling are plagued by the “curse of dimensionality,” in which there are more variables than observations. This is especially true when developing functional regression models where the independent dataset is some type of spectral decomposition, such as data from near-infrared spectroscopy. While we could develop a very complex model by simply taking enough samples (such that n > p), this could prove impossible or prohibitively expensive. In addition, a regression model developed like this could turn out to be highly inefficient, as spectral data usually exhibit high multicollinearity. In this article, we propose a two-part algorithm for selecting an effective and efficient functional regression model. Our algorithm begins by evaluating a subset of discrete wavelet transformations, allowing for variation in both wavelet and filter number. Next, we perform an intermediate processing step to remove variables with low correlation to the response data. Finally, we use the genetic algorithm to perform a stochastic search through the subset regression model space, driven by an information-theoretic objective function. We allow our algorithm to develop the regression model for each response variable independently, so as to optimally model each variable. We demonstrate our method on the familiar biscuit dough dataset, which has been used in a similar context by several researchers. Our results demonstrate both the flexibility and the power of our algorithm. For each response variable, a different subset model is selected, and different wavelet transformations are used. The models developed by our algorithm show an improvement, as measured by lower mean error, over results in the published literature.     

Some challenges for statistics

The paper gives a highly personal sketch of some current trends in statistical inference. After an account of the challenges that new forms of data bring, there is a brief overview of some topics in stochastic modelling. The paper then turns to sparsity, illustrated using Bayesian wavelet analysis based on a mixture model and metabolite profiling. Modern likelihood methods including higher order approximation and composite likelihood inference are then discussed, followed by some thoughts on statistical education.     

基于回归组合技术的连续性抽样估计方法研究

在使用样本轮换的连续性抽样调查中,不仅可以利用前期调查的研究变量的信息,还可使用现期调查的辅助变量信息来建立回归模型进行回归估计,进而构造回归组合估计量,并在此基础上确定最优样本轮换率和最优权重系数,使得回归组合估计量的方差最小,从而更大程度地提高连续性抽样调查的估计精度。     

城乡居民消费结构变动影响因素的比较分析——基于PLSR的阶段性证据

居民消费结构变动的影响因素可以根据新兴古典经济学的分析框架进行分析。虽然没有与专业化水平、交易效率和经济绩效直接对应的数据，但是可以选择一组涵盖三个方面的指标，运用偏最小二乘回归方法进行实证研究。基于1978～2005的数据，对中国城乡居民消费结构变动的影响因素进行比较分析，其结果显示了影响因素的阶段性差异。     

Non-parametric Analysis of Covariance – The Case of Inhomogeneous and Heteroscedastic Noise

Abstract.  The purpose of this paper was to propose a procedure for testing the equality of several regression curves f _i in non-parametric regression models when the noise is inhomogeneous and heteroscedastic, i.e. when the variances depend on the regressor and may vary between groups. The presented approach is very natural because it transfers the maximum likelihood statistic from a heteroscedastic one-way analysis of variance to the context of non-parametric regression. The maximum likelihood estimators will be replaced by kernel estimators of the regression functions f _i . It is shown that the asymptotic distribution of the obtained test-statistic is nuisance parameter free. Asymptotic efficiency is compared with a test of Dette & Neumeyer [Annals of Statistics (2001) Vol. 29, 1361–1400] and it is shown that the new test is asymptotically uniformly more powerful. For practical purposes, a bootstrap variant is suggested. In a simulation study, level and power of this test will be briefly investigated and compared with other procedures. In summary, our theoretical findings are supported by this study. Finally, a crop yield experiment is reanalysed.     

中国老年前期女性红细胞比积正常参考值与地理因素的关系

为制定中国老年前期女性红细胞比积正常参考值的统一标准提供科学依据,收集了中国229个地区用温氏法测定的17562例健康老年前期女性红细胞比积正常参考值,并对其与地理因素的关系进行了研究,结果发现海拔高度是影响老年前期女性红细胞比积正常参考值最主要的因素,随着海拔高度的逐渐增大,老年前期女性红细胞比积正常参考值也在逐渐的增大,相关性很显著。为此用因子分析的方法推导出了一个回归方程,如果知道了中国某地的地理因素,就可以用回归方程估算这个地区的老年前期女性红细胞比积正常参考值。依据老年前期女性红细胞比积正常参考值与地理因素的依赖关系把中国分为青藏区、西南区、西北区、东南区、华北区、东北区。     

国内删失数据统计研究状况综述

研究了国内在线性回归模型、非线性回归模型、半参数回归、非参数回归、单指标回归、生存分析、时间序列分析、密度估计等领域删失数据统计研究状况。